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Global field

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Summary

A finite extension of Q\mathbb Q, or a finite extension of the one-variable rational function field Fq(t)\mathbb F_q(t).

Record metadata

Carrier(s)

Axioms / constraints

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Incoming relations (arrows to this concept)

Each relation below ends at this concept.

FieldGlobal field

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Require a finite extension of QQ or Fq(t)F_q(t).

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Global fieldAdele ring

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

The adeles combine all local completions with an integrality restriction at almost all finite places.

How to interpret this relation type

Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.

Relation sources